Project 1; math 132 | Mathematics homework help

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Project 1;  Math 132
date

Name:____________________________________                 

Please write out the following statement and sign it.

I acknowledge that I have fully complied or will comply with all aspects of the University’s Honor Code in submitting this work.  All work on this project is my own.  I did not discuss this project with anyone except for the instructor.  I understand that work that is not typed or stapled will receive a grade of 0.  

                                                                                               

 ________________________________signature

General Directions:

  • The coversheet is to be stapled to all of your work.  Work will not be accepted if it is not stapled.
  • The work for this project is to be well organized. 
  • Graphs should be on graph paper and identified as to what the graph is.  Graphs are to be hand drawn, no computer generated graphs.
  • Use a full sheet of graph paper for each graph.  Select a scale and place the x and y axes in such a way that the graph is using most of the sheet of paper.  When referring to a graph in the written portion of this project, it should be referenced by its name.
  • The scale on the horizontal and vertical axes for the graphs must be consistent.  Values on the both scales must be labeled periodically.
  • The written summaries for this project should be typed.  Computations can be hand written, but they should be in the appropriate places.  This will require leaving space in the Word document to write the computations in.  All written summaries should use complete sentences and correct grammar.  Written computations MUST be inserted within the document at the appropriate places.
  • It is important that all work is in the order stated.  The only thing that can be out of order are the actual graphs.

 

Table for determining the value of B to use:

 

 

A

11

12

13

14

15

16

17

18

19

B

1879

2104

1348

1499

2316

2187

1894

1289

1579

 

 

 

 

 

 

 

 

 

 

A

20

21

22

23

24

25

26

27

28

B

1875

1583

1197

1157

1627

2179

1487

1955

1535

 

 

 

 

 

 

 

 

 

 

A

29

30

31

32

33

34

35

36

37

B

1554

1359

1612

1085

1158

1287

1487

1287

2454

 

Setting:   You are making prime magic wands using phoenix feathers.  The price and Cost are given at the bottom of the page.  You will need to use what we have been studying about quadratic functions to complete this project.  See the coversheet for general directions.

1.       Find R(x)

2.        Find the x intercepts, y intercept and vertex for R(x).  Show all computations.  Values must be exact.

3.       Graph R(x).  To graph R(x) use the information found above and plot at least 2 additional points to get a good graph.  Provide a table with the graph giving the points found in part 2 as well as the additional 2 points.  Put this table on the same sheet as the graph.  Remember the graph must be hand drawn on a full sheet of paper.

4.       Discuss what the graph of R(x) reveals about the revenue for this company.  What is an appropriate domain for the revenue function?  Think about this, what values yield realistic values for the revenue.  This function represents the money coming into the company.  So including negative x values or values that yield a negative revenue would not be appropriate.  This answer is to be an interval, not a single value.  Discuss why this the appropriate domain.

5.       Find the profit function, P(x), for this company.  (The work to find this function must be provided in the appropriate place.)

6.       Find the x intercepts, y intercept and vertex for P(x).   Work must be given.  Values must be exact.

7.       Graph P(x).  To graph P(x) use the information found above and plot at least 2 additional points to get a good graph.  Provide a table with the graph giving the points found in part 6 as well as the additional 2 points. 

8.       Discuss what the graph of P(x) reveals about the profit for this company.  Does it give an indication as to a cap for how large the production should be?  (IE, is there a value where if more is made the company loses money?)   Why is that the value you selected for the maximum production level?  Is there a minimum level of production that the company should have?  Why?  What is the break even quantity?  What does this break even quantity indicate about the desired production levels for this company?

9.    If the current production level is 350 wands a week, should you increase the production by 10%?  Why or why not?

 

 

For the price and Cost functions:  The value for A can be found by looking in the grade book on Blackboard (THE VALUE OF A IS 31).  It is identified as “Constant A”.  To determine your value for B refer to the table on the previous page.

 

This chart indicates how the project will be graded.  This page does not need to be included with the submitted project.

 

 

Correct Value

Comments

Score

Following General Directions on Coversheet.

 

 

/6

R(x)

 

 

/2

X intercepts for R(x)

 

 

/2

Y intercept for R(x)

 

 

/2

Vertex for R(x)

 

 

/2

Graph for R(x)

 

 

/3

Discussion Related to R(x) – What does it tell you about the revenue

 

 

/2

R(x) domain

 

 

/2

P(x) is correct

 

 

/2

X intercepts for P(x)

 

 

/2

Y intercept for P(x)

 

 

/2

Vertex for P(x)

 

 

/2

Graph of P(x)

 

 

/3

Discussion related to P(x)

 

 

/2

Cap related to  production

 

 

/2

Minimum level of production

 

 

/2

Break even quantity

 

 

/2

Making 280 – make more?

 

 

/2

TOTAL

 

 

 

/42

 

 

Test 1:  MATH 132

The test covers Chapter 1 sections 1 – 3, Chapter 2 sections 1 – 4.

On Test day all book bags, books, notebooks, etc. are to be left at the front of the room.  The only items that you are allowed to have at your desk is your graphing calculator, pencil and straight edge for graphing.  Tests will be collected after 50 minutes, there will not be any extended time.

Calculators may be checked for unauthorized material such as formulas, etc.

Questions from 1-3 will not require you to do regression on your calculator.

·         Interval, inequality, and number line graphs

·         Solving inequalities

·         Equations for lines

·         Slope formula, slope-intercept form, standard form for lines

·         Parallel and perpendicular lines

·         Cost, Revenue, Profit

·         Variable cost, fixed cost

·         Break even quantity

·         Price-supply equations (example 8, page 21)

·         Function – is it or isn’t it

·         Function notation

·         Vertical and horizontal transformations of functions

·         Reflection of functions around the x axis

·         Quadratic functions – vertex, open, max/min;  applications related to quadratics

·         Polynomial functions – graph, identify minimum degree given the graph

·         Rational functions – graph

·         Find the x intercepts for a function using the CALC feature on the calculator.

·         Find the intersection of two functions using the CALC feature on the calculator.

 

The following problems are just a starting point for your review.

 

 

1.  Solve and give the answer in interval form.

             

 

2.  Solve for x.  Give the answer in algebraic form.

             

 

3.  Find the equation of the line that goes through the point (2, -6) with a slope of 4.  Give the answer in slope-intercept form.

 

4.  Find the equation of the line that goes through the point (1, 9) and is perpendicular to the line y = 6x – 2.  Give the answer in slope-intercept form.

 

5.  The linear regression line model for the height of balsam fir trees is h = 3.9d +18.73, where d is the diameter at 4 feet above the ground in inches, and h is the height of the tree in feet.

            a)  Using this model, how tall is a tree with a diameter of 5 inches?

            b)  Using this model, what is the diameter of a tree that is 53 feet tall?

 

6.  State the domain and range:

a)     (domain only)                      b)   (domain only)

c)                                             d)  

X

-2

4

7

2

 

x

-1

3

2

8

-4

2

Y

4

8

4

4

 

y

0

5

-2

9

7

4

 

e)     5                8                                  f)  7                 

      4                3                                     -3                  9

                        11                                    1                  4

      2                -3

 

7.  For the relations above in #6, which ones are functions.

 

8.      Find the following

 

9.  The graph of  is translated up 3 units and 5 units to the right.  What is it’s equation?

            There will also be dot to dot problems like were done in class.

 

10.  Ahava Manufacturing makes speakers for cell phones.  Each speaker sells for p = 15-0.2x.  The cost function is .  What is the profit function?  For what range of values does the company make a profit?  If the company is currently making 10 speakers, and they plan to increase their production by 10%, would you encourage them to do this or not?  Why?

 

11.   For these revenue and Cost functions, what is the break even quantity?

             

 

12.  Sketch the graph of the following functions.  The x intercepts and y intercepts must be labeled with the correct exact values.  Find any vertical asymptotes as is appropriate.

a)   

b)   

 

 

 

 

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